Just patched my laptop using a cellphone teather and had zero issues. It did take about 3 or 4 minutes to patch through the final .hogg file but then ended. When the launcher is patching hit X and it will show you which files it is working on.
Its not really broken, Its just the way they choose to show the data thats misleading.
The patcher says: 200mb lets say but in actual fact its only downloading say 50mb. What the 200mb is, is the Installed HD space the patch will take when its decompressed into STOs folder.
Its a stupid way of doing it because lets face these days who only has 200mb left on there drives. If they wanted to go with a better idea they could say: Patch 50 mb, 200mb disk space required.
Regards it getting stuck. If it happens to me or its going slow. I quit launcher (It will resume) I then quit the net with the disable connection, I then switch off my router 20 seconds and re-enable router and connection. On doing this it gives me a new IP address which usually helps.
Also you can go to options when you have entered your password in the launcher and set the proxy to US/EU and None. Try what's best for you. make sure you tick; Download Patch with Proxy or something to that effect.